Multiply and Divide Rational Expressionslehimath.weebly.com/.../6.1_multiply,_divide_rational_expressions.pdf · Rational Expressions - Simplify Rational expressions can be simplified

Multiply and Divide

Rational ExpressionsLESSON 6.1

Objective

Determine the domain of rational

expressions and functions

Simplify, multiply, and divide rational

expressions and functions

Rational Expressions

A rational expression is the quotient (÷) of

two polynomials

EX: 𝑥−5

2𝑥+1

𝑥2−7𝑥−18

𝑥2−4

1

𝑥−3

2𝑎2+5𝑎𝑏+2𝑏2

𝑎2−6𝑎𝑏+8𝑏2

Rational Expressions - Domain

REMEMBER: We cannot ÷0

Domain consists of all real numbers

except those for which the denominator

is zero.

Rational Expressions - Domain

Determine the domain for each of the

following rational expressions

A. −3𝑧

𝑧+5B.

𝑛2−2𝑛−8

𝑛2−𝑛−12

Rational Expressions - Domain

Determine the domain for each of the

following rational expressions

C. 𝑅 𝑥 =𝑥−3

𝑥2−2𝑥−8

Rational Expressions - Simplify

Rational expressions can be simplified by

dividing out any common factors

EX: 10

10= 1

𝑥

𝑥= 1

𝑥−3

𝑥−3= 1

2 𝑥−3

3(𝑥−3)=

2

3

Rational Expressions - Simplify

Simplify

D. 𝑥2+𝑥−6

2𝑥2−5𝑥+2E.

𝑦3+27

2𝑦2+6𝑦

Rational Expressions - Multiply

MULTIPLYING RATIONAL EXPRESSIONS

1. Completely factor each polynomial

2. Divide out common factors

3. Multiply remaining terms (fractions)

Rational Expressions - Multiply

F. 𝑛2−9

𝑛2+5𝑛+6×

𝑛+2

−2𝑛+6

Rational Expressions - Multiply

G. 𝑎2−𝑏2

10𝑎2−10𝑎𝑏×

10𝑎+5𝑏

2𝑎2+3𝑎𝑏+𝑏2

Rational Expressions - Divide

DIVIDING RATIONAL EXPRESSIONS𝑎𝑏𝑐𝑑

=𝑎

𝑏÷𝑐

𝑑=𝑎

𝑏×𝑑

𝑐

KFC→Keep the First, Flip the Second, Change the Sign

Rational Expressions - Divide

H.

45𝑧4

7𝑦5𝑧

21𝑦2

Rational Expressions - Divide

I.

𝑝3−8

5𝑝2+15𝑝

𝑝2−4

𝑝2+3𝑝

Rational Expressions - Functions

Sometimes we are given two or more

functions and told to combine and

simplify them.

EX: 𝑓 𝑥

𝑔 𝑥𝑓 𝑥 ⋅ 𝑔(𝑥)

Rational Expressions - Functions

J. 𝑓 𝑥 =𝑥2−9

2𝑥2−8𝑥𝑔 𝑥 =

𝑥−4

𝑥2+4𝑥+3ℎ 𝑥 =

𝑥2+6𝑥+9

𝑥2−5𝑥

1. Find 𝑓 𝑥 ⋅ 𝑔(𝑥)

2. Find 𝑓 𝑥

ℎ 𝑥